Prepared for submission to JCAP

Looking for ancillary signals aroundGW150914

Rahul Maroju,a Sristi Ram Dyuthi,a Anumandla Sukruthaa andShantanu Desai, b,1

aDepartment of Electrical Engineering, IIT Hyderabad, Kandi, Telangana-502285, IndiabDepartment of Physics, IIT Hyderabad, Kandi, Telangana-502285, India

E-mail: ee15btech11018@iith.ac.in, ee14btech11031@iith.ac.in,ee14btech11002@iith.ac.in, shantanud@iith.ac.in

Abstract. We replicated the procedure in Liu and Jackson [1], who had found evidence for alow amplitude signal in the vicinity of GW150914. This was based upon the large correlationbetween the time integral of the Pearson cross-correlation coefficient in the off-source regionof GW150914, and the Pearson cross-correlation in a narrow window around GW150914, forthe same time lag between the two LIGO detectors as the gravitational wave signal. Ourresults mostly agree with those in Liu and Jackson [1]. We find the statistical significance ofthe observed cross-correlation to be about 2.5 σ. We also used the cross-correlation methodto search for short duration signals at all other physical values of the time lag, within this4096 second time interval, but do not find evidence for any statistically significant events inthe off-source region.

1Corresponding author.

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Contents

1 Introduction 1

2 Recap of LJ16 2

3 Data Conditioning of GW150914 3

4 Results from band-passing and notch filtering 54.1 Correlation between CGW and D 6

5 Results after band-pass filtering and whitening 6

6 Cross-correlations after removing the GW signal 9

7 Estimation of significance 12

8 Conclusions 13

1 Introduction

Three and half years ago, there was a watershed moment in astronomy with the detection ofgravitational waves, by the LIGO detectors, starting with the first binary black hole merger,viz. GW150914 [2]. Since then, the LIGO-VIRGO collaboration (LVC) has detected a total ofseven binary black hole mergers [3–7] and one binary neutron star merger [8]. These detections(which led to the 2017 Nobel Prize in Physics) have provided a plethora of informationabout astrophysics, nuclear physics, modified theories of gravity, r-process nucleosynthesis,Hubble constant, etc (eg. [9–15] and references therein). Along with the discoveries, the LIGOopen science center (LOSC) has publicly initially released the strain data around each of thedetections, and later the full science-mode data from the first two observing runs [16].

Nevertheless, a few groups have still raised a few concerns about some of the LIGOdetections [17, 18]. For example, Creswell et al [18] used data from LOSC around GW150914to point out that the calibration lines and also the residual noise show a peak in the cross-correlation at the same time lag as the original signal. However, at least two groups havebeen unable to reproduce these results, and therefore dispute these claims [19, 20] (see how-ever [21]). Conversely, some other groups have found evidence for additional signals andanomalies potentially pointing to new Physics [1, 22–24]. In Refs. [22, 23], the authors haveargued for a tentative evidence for echo signals post the merger of the compact objects in boththe binary black hole and neutron star events. This work has also received a lot of attentionand many groups have tried to reproduce these claims [20, 25, 26]. In Ref. [24], the authorshave applied a regularization-based denoising technique to the data around GW150914 andfound that the reconstructed waveforms disagree at the high frequency end with the GR-basedbinary black hole template waveforms. Liu and Jackson [1] (LJ16 hereafter), calculated thePearson cross-correlation coefficient for data from Hanford and Livingston detectors in thestrain data covering 4096 seconds around GW150914. Using this analysis, they have founda tentative evidence (3.2σ) for a signal 10 minutes before GW150914, lasting for about 45minutes with the same time lag as GW150914.

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Within the LVC, the GW150914 signal was detected by two independent pipelines: oneof which involves a matched filtering search from coalescing binaries and the second searchinvolving a model-independent search for short duration signals of any waveform morphol-ogy, known as “bursts”. Different burst search algorithms, which look for waveform-agnostictransients in LIGO data do not always detect the same triggers [27]. Therefore, given theimportance of gravitational wave detections for physics and astronomy, it is important toverify any concerns about any of the detected events, as well to corroborate any additionalsignals found by people outside LVC, using independent analysis techniques.

Here, we try to reproduce the claims in LJ16, by trying to mimic their procedure asclosely as possible. We also look for short-duration transient signals at all time lags using asimple extension of the method used in LJ16. We note that most recently Nitz et al [28] havecarried out a matched filter search (with coalescing binary signals as templates) over the fullO1 data and do not find any additional GW signals, beyond those reported. These signals werealso not found in the recent re-analysis by the LVC [7]. While this work was in preparation,Nielsen et al. [20] have written a rebuttal countering the claims in Ref. [18] (which is follow-up paper to LJ16), where-in they have also used the Pearson cross-correlation coefficient toexamine data around ±512 seconds of data around GW150914 signal. However, none of theseworks have tried to reproduce all the claims in LJ16, or replicated their procedure, therein,which is our goal.

The outline of the paper is as follows. We first briefly recap the results of LJ16 inSect. 2. We describe the two independent data conditioning steps carried out in Sect. 3. Wedescribe the results from these two steps in Sects. 4 and 5 respectively. We then re-analyzethe cross-correlations after removing the best-fit GW signal and these results can be foundin Sect. 6. Finally, our estimation of significance using Monte-carlo simulations is discussedin Sect. 7. We conclude in Sect. 8. We have also uploaded our analysis code on github anda web link can be found in Sect. 8.

2 Recap of LJ16

LJ16 downloaded ±2048 seconds of Hanford and Livingston data (sampled at 16 kHz) aroundGW150914, starting at GPS time 1126257414. Very simple data conditioning was imple-mented [29] along the same lines as done by the LVC. The data was band-pass filtered be-tween 50 and 350 Hz using a butterworth filter for the primary analysis. However later,they explored the sensitivity of their significance to different bandwidths. Narrow lines (cor-responding to power, calibration and violin mode resonances) were removed in the Fourierdomain by clipping the amplitudes to zero power [18]. The final time-series used to searchfor gravitational waves was then inverse Fourier transformed. A total of 30 seconds of datawas excluded at both the ends to avoid boundary artifacts. LJ16 then calculated the func-tion C(t, τ, w) between the time streams of the two LIGO detectors based upon the Pearsoncross-correlation coefficient as a function of the time lag (τ), duration of the signal (w). It isdefined as follows [1]:

C(t, τ, w) = Corr(Ht+w+τt+τ , Lt+wt ) (2.1)

Corr(x, y) =

∑i(xi − x)(yi − y)√∑

i(xi − x)2∑

i(yi − y)2(2.2)

where xi and yi are the time-samples over which Pearson cross-correlation coefficient is cal-culated; Ht+w+τ

t+τ is the Hanford time-series data from (t+ τ → t+ τ +w) seconds; and Lt+wt

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is the same for Livingston data from (t → t + w) seconds. We then define C(t, τ, w) forGW150914, which we refer to as CGW (τ, w) as follows

CGW (τ, w) = Corr(HtGW+w+τtGW+τ , LtGW+w

tGW) (2.3)

We note that a similar statistic was previously used as a signal consistency test in the post-processing pipeline for LIGO burst searches during science runs S2, S3, and S4 [30–32], underthe moniker r-statistic [33] or CorrPower [34]. This pairwise cross-correlation posits simi-larity of the signals (modulo any offsets in calibration). This ansatz is valid for the LIGO de-tectors, as the 4 km Livingston interferometer is maximally aligned with the Hanford detectorsto the extent allowed by Earth’s curvature (modulo a sign flip in one of the detectors, whichmakes the signals anti-correlated) [35]. For mis-aligned detectors, Pearson cross-correlationcannot be used and needs to be replaced by Rakhmanov-Klimenko cross-correlation or similarvariants [36].

In LJ16, cross-correlation has been run in extremely short-duration non-overlapping timewindows (0.1 seconds) as well as over data stretches as long as 30 minutes. In Ref. [20], thewindow duration for calculating cross-correlation was chosen to be 0.2 seconds. To look forweak-amplitude signals, LJ16 introduced the functional D(τ), related to the integral of thecross-correlation and is defined as [1]

D(τ) =1

t2 − t1

∫ t2

t1

C(t, τ, w)dt (2.4)

where w is the duration of the signal. In LJ16, w was chosen to be 0.1 seconds, but we considerw values of both 0.1 and 0.2 seconds. Note that GW150914 lasted for about 0.2 seconds withfrequency sweeping from 35 to 150 Hz over this duration. The main premise in positing theabove statistic is that with an increasing window duration, the contribution of noise shoulddecrease, whereas even a weak signal would add up coherently. They also considered thecross-correlation of CGW (τ, w) (from Eq. 2.3) and D(τ), (where D(τ) is calculated over atime interval from t1 to t2), which they refer to as E(t1, t2) and is defined as

E(t1, t2) = Corr{CGW (τ, w), D(τ)} for τ ∈ (τ1, τ2) (2.5)

When D(τ) and C(t, τ, w) were applied to a time stretch of data, 30 minutes before and afterthe signal (after excluding ±60 seconds of data around GW150914), argmax

τ|C(t, τ, w)| =

argmaxτ

= |D(τ)| = 6.9 ms. A more precise estimate of the start and stop time of this ancillary

signal (in the GW150914 off-source interval) was then obtained by adjusting the start andstop time, as well as by searching in narrow-band filters, until E(t1, t2) is maximized. Thestart time of the signal was thereby estimated to be 1280 seconds after the beginning of thestarting time stamp (or about 10 minutes before GW150914) and ends 45 minutes later. Thestatistical significance was estimated by calculating the above statistics for 20,000 differenttime-shifts with absolute value > 10 ms. This estimated statistical significance was about3.2σ.

3 Data Conditioning of GW150914

For our analysis, we downloaded 4096 seconds of data around GW150914, sampled at 4096Hz, using version 2 calibration (dubbed v2 and released in October 2016), starting at GPS

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time 1126257414 (Mon Sep 14 09:16:37 GMT 2015). This start time is about 2048 secondsbefore the GW150914 signal. This same calibration strain data file was also used in therecent re-analysis in Ref. [20]. Although, the results in LJ16 were obtained using v1 of thecalibration, Ref. [20] has shown that the results are not sensitive to the calibration version.Therefore, we stick to v2 of the calibration data for this analysis.

Data conditioning for the event is done in the same way as described in the originalGW150914 tutorial on the LOSC webpage https://www.gw-openscience.org/s/events/GW150914/GW150914_tutorial.html. Note that on this tutorial webpage, it has been shownthe signal is visible using two independent data conditioning procedures. The first procedureinvolves whitening in the frequency domain followed by band pass filtering (in the time-domain using a butterworth filter). Whitening in the frequency domain is mathematicallyequivalent to dividing the input data in the Fourier domain by its amplitude spectral density.This whitened frequency domain data is then transformed back to the time domain, whichis then used for GW analysis. Alternately, the signal is also visible from the same band-pass butterworth filter, followed by application of IIR notch filtering in the time domain toget rid of various lines. As mentioned earlier, this signal was seen by both the burst andcompact binary coalescence-based matched filtering search pipelines, which look for inspiraland merger of compact stellar remnants, also known as “CBC” within the LVC [37, 38].The burst search was done using two pipelines, coherent Waveburst (cWB) [39] and alsoomicron-LALInference-Bursts [40]. The cWB algorithm uses a linear predictive error filter,which is equivalent to whitened time series [39]. The CBC search was also carried out usingtwo pipelines, called PyCBC [41] and GstLAL [42]. Both these pipelines employ a whiteningfilter in the data conditioning steps.

As discussed in Sect. 2, LJ16 have applied a band-pass window followed by notch win-dows, obtained using clipping in the frequency domain. We also note that in the Block-Normalburst search pipeline [43], which was used until S5 [44], data conditioning consisted of all threesteps (band-passing, whitening and line removal) [45]. In some other pipelines, the data hasbeen whitened using a running median [46].

Therefore, there is no unique data conditioning procedure followed by the different GWsearch algorithms. Here, we present our results using both band-pass and notch filtering (forline removal), as well as using band-pass and whitening. Ref. [20] have also done their analysisusing notch filtering as well as whitening. The code for implementing these steps has beendescribed on the aforementioned LOSC webpage. We now briefly describe both these steps.

We first apply FFT to the full 4096 seconds of data. We then apply a bandpass filterbetween 50 Hz and 350 Hz to suppress the low-frequency noise (mainly due to seismic activity)and high frequency noise (mainly due to quantum noise) [47]. The noise floor shows a steep risein this frequency range [48], and hence the signal is always band-passed in this intermediatefrequency range to search for astrophysical signals. The band-passing is implemented usinga linear butterworth filter. The LIGO noise spectrum also contains a number of lines in thefrequency domain due to mechanical resonances, power line harmonics, etc [47]. These havebeen removed using IIR based time-domain notch filtering, following the algorithm on theabove webpage. The list of lines for which the notch filter has been applied include 14, 34.7,35.3, 36.7, 37.3, 40.95, 60.0, 120.0, 179.99, 304.99, 331.49, 510.02, 1009.99 Hz respectively.The same lines have also been notch-filtered in a follow-up paper by Creswell et al. [18].Results from this data conditioning procedure are described in Sect. 4.

For our second set of results, instead of notch-filtering, we applied a whitening filter, bydividing by the noise spectrum in the frequency domain using the same code as mentioned

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on the above LOSC tutorial website.

4 Results from band-passing and notch filtering

Here, we describe our results after the application of band-pass filtering and notching. Thecorresponding results after the application of the whitening filter, instead of the notch filtershall be described in Sect. 5.

Similar to LJ16, we exclude the first and last 30 seconds of the data. Using this data, wefirst calculate CGW (τ, w) as a function of the time lag (τ) between the two LIGO detectors ina ± 0.2 second window around GW150914 corresponding to the GPS time of 1126259462.42(Sep 14 09:50:45). Since we have downsampled the data to 4 kHz, the minimum resolutionin the time lags we can have is 0.246 milliseconds. This plot can be found in Fig. 1 and issimilar to Fig. 1 of LJ16 or the corresponding plot in Fig. [20]. One can see a sharp dip for atime lag close to 7.33 ms corresponding to the signal. Note that unlike LJ16, we do not finda minimum value of τ closer to 6.9 ms. The peak absolute value of C is at ∼ 7.33 ms, closerto the value found in Ref. [20]. The uncertainty in the peak time is about 0.246 milliseconds,which is limited by the downsampled frequency of 4 kHz. Similar to LJ16, we then calculatedD(τ) (from C(t, τ, w)) for a long time stretch of data spanning 30 minutes before and afterthe GW signal, after excluding the data within ±60 seconds around GW150914. We thenoverlay this along with CGW for w = ±0.05 seconds around GW150914. Note that for thispurpose similar to LJ16, both CGW and D have been rescaled, so that they have a meanvalue of zero and a rms value of one. To calculate D, one needs to integrate C(t, τ, w) overa window duration. For the calculation of D, we calculated C in both 0.1 and 0.2 secondwindows. These plots for CGW and D using both the windows can be found in Figs. 2 and 3.We find roughly the same behaviour as in Fig. 1 of LJ16. In the panels showing the data afterGW150914, we find a near-maximal correlation (similar to LJ16) between CGW and D at thesame time lag as GW150914. However, we also find a similar correlation at the opposite endfor τ between -7 and -10 ms. Therefore, it is not immediately obvious if the strong correlationbetween CGW and D at the same time lag as GW150914 is pointing to a post-merger signal.

As an extension of this technique, we then look for additional short duration signalslasting 0.1 and 0.2 seconds using the cross-correlation method, which may appear at arbitrarytime lags. Furthermore, if there is a persistent long-duration signal, then C should have thesame value across many 0.1/0.2 second chunks. For this purpose, we calculated the cross-correlation in each 0.1/0.2 second chunk for the entire 4096 seconds of LIGO data, for timelags ranging from -10 to 10 milliseconds. These plots can be found in Fig. 3 and Fig. 4.The maximum (absolute) value of C is seen at the peak of GW150914. We do not find anyvalues of C as large as that for GW150914 at any other times. For the 0.1 second window,the maximum cross correlation in the off-source region has a value of 0.63 at the GPS timeof 1126257962.4, about 548 seconds from the start of the time series or 1500 seconds beforeGW150914. For the 0.2 second window, the maximum absolute cross correlation in the off-source region equal to -0.47 occurs at the GPS time of 1126259229.4, about 1815 secondsfrom the start of our time series, or 233 seconds before GW150914. The maximum (absolute)values of C at the peak of GW150914 are -0.7 and -0.87 for the 0.2 and 0.1 second windowsrespectively.

Therefore, with this data conditioning procedure, we roughly agree with the results inLJ16, although we also find a strong correlation between CGW and D for time lags close to-10 ms, which is far from the time lag seen for GW150914. However, when we scanned the

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E(1280, 1988) E(2108, 4050) E(1280,1988)⋃(2108, 4050)

τ ∈ (5 ms, 9 ms) 0.147 0.946 0.831

τ ∈ (-10 ms, -6 ms) -0.976 0.969 -0.523

τ ∈ (-9 ms, -5 ms) -0.989 0.898 -0.259

τ ∈ (-10 ms, -10 ms) 0.371 0.664 0.775

Table 1. E (defined in Eq. 2.5) over different time windows (columns) and for different time lags(rows). This is analogous to Table I of LJ16 [1], except that we have removed data within ± 60seconds of GW150914 for calculating D. Our results mostly agree with the corresponding table inLJ16.

full 4096 seconds of data around GW150914, we do not find any other value of C calculated insmall duration windows, whose absolute value is as large as GW150914, for both the windows.

4.1 Correlation between CGW and D

To further pin down the exact start and end time of the signal, LJ16 calculated E (cf. 2.5)by calculating the cross-correlation between CGW and D. They find that E is maximized,when the signal starts at 1280 seconds and ends at 4050 seconds from the start of the down-loaded data segment. We calculated the values of E for the same starting and ending times asLJ16 from 1280 to 4050 seconds. Note however that unlike LJ16, we have excluded the datawithin ±60 seconds around GW150914, for evaluating D, in order to avoid any bias from theGW signal in the final value for E1. Therefore, instead of E(1280, 2048), E(2048, 4050), andE(1280, 4050), we evaluatedE(1280, 1988), E(2108, 4050), andE(1280, 1988)

⋃E(2108, 4056).

Given the similarity in the trends of CGW and D for time lags close to -10 ms, we also checkedthe value of E for τ ∈ (−10,−6) ms and τ ∈ (−9,−5) ms. These values of E can be foundin Table 1. Similar to LJ16, we find that E(2108, 4050) is largest for τ ∈ (5,9) ms, and forτ ∈ (-10,10) ms, E is largest for t1 = 1280 and t2 = 4050, even after excluding ± 60 secondsaround GW150914. Therefore, our results for E are broadly in agreement with those in LJ16,even after excluding ±60 seconds of data around GW150914 signal. However, we also finda value for E(2108, 4050) very close to one for τ ∈ (−10,−6) ms. If there was an externalancillary post-merger signal at the same time lag as GW150914, then we cannot think of anyapriori reason why E should be close to one for a time lag close to -10 ms.

We then repeat the test carried out in LJ16 by band-passing the data into contiguous20 Hz bands between 30 Hz and 150 Hz. These values for E in different bands can be foundin Table 2. Our results agree with Table II in LJ16. We also find that the correlations in50-70 Hz and 90-110 Hz are very close to 1.

Therefore, to summarize, our results for E broadly agree with those in LJ16, for thesame time lag as GW150914 (7.5 ms). But we also find a large value for E at time lagsbetween −10 and −6 ms.

5 Results after band-pass filtering and whitening

We now go through the same exercise as in Sect. 4, after skipping the notch filtering step, butreplacing it by whitening the data. We first calculate the cross-correlation in a ±0.2 second

1LJ16 found that excluding the data around GW150914 for the purpose of calculating E, does not changethe results in Section III B if their paper (H. Liu, private communication).

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Figure 1. Cross-correlation coefficient in a ±0.2 second window around GW150914 as a function oftime-lag between the Hanford and Livingston detectors. The dashed vertical line is for a time lag of7.33 milliseconds. We note that the data has been downsampled to 4096 Hz, so the minimum timeresolution is 0.246 milliseconds. For this plot, the data has been band-passed from 50 to 350 Hz andthen notch filtered.

Figure 2. Value of CGW (τ) and D(τ) in a 30 minute time window (starting from GPS time1126257444) until 60 seconds before GW150914 (left panel). The right panel shows the same for a 30minute time window starting from 60 seconds after GW150914. D has been calculated by integratingover the values of C(t, τ, w), for w = 0.2 seconds. The data conditioning is the same as in Fig. 1. Notehowever that CGW has been calculated in a ±0.05 second window around GW150914 and is slightlydifferent compared to Fig. 1. Both CGW and D have been rescaled so that they have a mean value ofzero and rms value of one. We notice that in the right panel CGW and D are correlated around thesame time lag as GW150914 (in agreement with LJ16) but also for time lags close to -10 ms.

window around GW150914 , and the resulting figure can be found in Fig. 6. Again, we see apeak at around 7.33 milliseconds. We then calculate CGW and D for the same time windowas in Figs. 2 and 3. These plots for 0.1 and 0.2 second signal durations can be found in Figs. 7and 8. Again, the qualitative trends are similar to those in Figs. 2 and 3, and similar toLJ16, we see a strong correlation between CGW and D at the same time lag as GW150914,for a 30 minute stretch of data after GW150914. However, for the same data, we also noticea correlation between CGW and D for τ between -7.5 and -10.0 ms.

Finally, the values of C in 0.1 and 0.2 second chunks are shown in Figs. 9 and 10. We

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Figure 3. Same as Fig. 2, except that D has been calculated for a 0.1 second window. Ourconclusions are same as in Fig. 2.

Figure 4. Maximum values of the cross-correlation coefficient (C) after scanning over time lagsfrom -10 to 10 milli-seconds in each of these windows, over a time stretch of about 4000 secondsencompassing the GW150914 signal (t− tevent = 0 in the above plot). Data conditioning is same asin Fig. 1. We find that the maximum absolute value of C occurs at the peak of the GW150914 signaland there is no other statistically significant peak outside the vicinity of GW150914. The maximum(absolute) value of cross correlation is -0.703 and occurs in the batch with mid-instant 1126259462.48with τ equal to 7.32 ms, which corresponds to GW150914. In the off-source region (ignoring 60 secondsaround the GW event), the largest (absolute) value of C occurs 233 seconds before GW150914 witha value of -0.47.

do not find any other time interval with a value of C as large as that of GW150914. In theoff-source region and for a 0.1 second time interval, the maximum (absolute) cross correlationis about -0.82 and occurs at a GPS time of 1126259188.7, which is about 1774 seconds fromthe start of the time-series, or 274 seconds before GW150914. For the 0.2 second window,the maximum (absolute) cross correlation is about -0.68 and occurs at the GPS time of1126258623.6, which is about 1209 seconds from the start of the time series, or 839 secondsbefore GW150914. The maximum (absolute) values of C at the peak of GW150914 are -0.76and -0.82 for the 0.2 and 0.1 second windows respectively.

Therefore, even after the application of a whitening filter (instead of notch filter) as partof the data conditioning step, the trends in C and D are in agreement with those in LJ16,

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Figure 5. Same as Fig. 4, except that C was calculated in 0.1 second window. Similar to Fig. 3,the peak occurs during the occurrence of GW150914 and no other value of C is close. The maximum(absolute) cross correlation is equal to -0.88 and occurs in the batch with mid-instant 1126259462.4with a corresponding τ of 7.32 ms, which corresponds to GW150914. In the off-source region, thenext largest (absolute) value of C occurs 1500 seconds before GW150914 with a value of 0.63.

Bandpass range (Hz) E(-10 ms, 10 ms)

30-50 0.813

50-70 0.913

70-90 0.212

90-110 0.996

110-130 0.426

130-150 0.514

Table 2. E(-10 ms, 10 ms) in various sub-bands for the time interval (1280, 4050) excluding ± 60seconds around the GW event. This is analogous to Table III of LJ16 [1] and our results are mostlyin agreement.

as well as our previous results discussed in Sect. 4. Based upon the values of C in 0.1 and0.2 second windows, we do not find evidence for any additional short duration signals in theoff-source region of GW150914.

6 Cross-correlations after removing the GW signal

In Sections 4 and 5, we have calculated the cross-correlation between D and Cgw, afterremoving ± 60 seconds of data around GW150914 in the calculation of D. Here, we redothe cross-correlation after including these 60 seconds, but after subtracting the gravitationalwave signal around GW150914. For this purpose, we subtracted the matched filter templatefrom the filtered data in a 0.45 seconds window starting from GPS time 1126259462 (Sep 1409:50:45 GMT 2015) 2, so that the full datastream used in the calculation of D is consistent

2For this analysis, we directly used the residuals provided by the LOSC, which are available at https://www.gw-openscience.org/s/events/GW150914/P150914/fig1-residual-H.txt and fig1-residual-L.txt

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Figure 6. Same as in Fig. 1, except instead of notch filtering, data has been whitened. Again, wefind a (negative excursion) peak at 7.33 milliseconds at the same time as the GW signal.

Figure 7. Same as Fig. 2, except that the data has been whitened instead of notch-filtered. D hasbeen calculated in 0.1 second batches. The correlation between CGW and D trends for the figure inthe right panel is same as in Fig. 2.

Figure 8. Same as Fig. 7, except that D has been calculated in 0.2 second windows. Our conclusionsare same as in Fig. 7.

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Figure 9. Same as Fig. 4, except that the data has been whitened, instead of applying a notchfilter. The largest (absolute) value of C is for GW150914. This maximum (absolute) cross correlationis equal to -0.76 and occurs in the batch with mid-instant GPS time of 1126259462.5 seconds, witha corresponding τ of 7.57 ms. In the off-source region, the largest (absolute) value of C occurs 839seconds before GW150914 with a value of -0.68.

Figure 10. Same as Fig. 9, except that C was calculated in 0.1 second window. The only peak isseen at the location of GW150914, as in the other plots. The maximum absolute cross correlation is-0.895 and occurs in the batch with mid-instant GPS time of 1126259462.4 seconds for τ equal to 7.56ms, which corresponds to the GW150914. In the off-source region, the next largest (absolute) valueof C occurs 274 seconds before GW150914 with a value of -0.82.

with noise. We show the trends for D (after using this data with the GW signal subtracted)in a time window from 1280 to 4050 seconds, along with CGW in Fig. 11. Similar to before,we see a strong correlation between D(τ) and CGW (τ).

We then repeat the same exercise as in Sect. 4.1 and calculate E in the same timewindows using this signal-subtracted data around GW150914. These results can be found inTable 3. The results are the same as in Table 1. We still see a value for E(1280, 4050) closeto one for τ ∈ (5, 9) ms and τ ∈ (−10, 10) ms.

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Figure 11. D(τ) in a time window from 1280 to 4050 seconds, by including the full data , aftersubtracting the signal around GW150914 using the best-fit matched filtering template, so that theresidual is consistent with noise. We find that similar to previous such figures, Cgw(τ) is stronglycorrelated with D(τ) for the same time lag as GW150914.

E(1280, 2048) E(2048, 4050) E(1280, 4050)

τ ∈ (5 ms, 9 ms) 0.118 0.949 0.838

τ ∈ (-9 ms, -5 ms) -0.954 0.932 -0.743

τ ∈ (-10 ms, -6 ms) -0.940 0.992 0.113

τ ∈ (-10 ms, -10 ms) 0.320 0.652 0.755

Table 3. Similar to Table 1, except that we have removed the GW signal from the data instead ofignoring the data around the GW150914, for calculating D. Our values for E are approximately thesame as in Table 1.

7 Estimation of significance

To estimate the statistical significance for our values of E in Sections 4.1 and 6, we time-shiftthe data from one of the detectors using unphysical time lags, in order to generate Monte-Carlo simulations for a pure noise floor. A similar procedure is usually used to estimate thesignificance of all thw GW detections by the LVC collaboration (cf. Ref. [2] for GW150914),and was also used by LJ16 to estimate the significance of their estimated values of E.

Here, we consider the Hanford data from 1280 to 4050 seconds. We then analyze theLivingston data with the same duration, but time-shifted with respect to Hanford data from(−600,−4) seconds in 20,000 steps.3 For each value of this time-shifted pair of data, wecalculate D(τ) for τ ∈ (−10,−10) ms. Each D(τ) is cross-correlated with Cgw(τ) to evaluateE. Each value ofE using this combination of data with unphysical time lags, can be consideredas the value for “null-stream” data with no signal and any value close to one, can only bebecause of a statistical fluctuation. The observed values of E for each of these realizationscan be found in Fig. 12.

The number of realizations, which exceed our observed value of E equal to 0.775 (cf.

3Note that in LJ16 to estimate the statistical significance, only one second of Hanford/Livingston dataseparated by unphysical time lags has been used (H. Liu, private communication).

– 12 –

Figure 12. A histogram of E(1280, 4050) calculated by shifting the Livingston data using unphysicaltime lags from -600 to -4 seconds in 20,000 steps. For each of these lags, E is calculated for τ ∈(−10, 10) ms The number of realizations resulting in E exceeding the thresholds 0.775, 0.755, 0.84are 126, 192 and 22 respectively corresponding to False alarm probabilities of 6.3× 10−3, 9.6× 10−3,and 1.1× 10−3 respectively.

Sect. 4.1) is equal to 126 out of 20,000, corresponding to a false alarm probability (FAP) of6.3 × 10−3 or a significance of 2.5σ. The number of realizations for which we get a value ofE greater then 0.755 (which we get after including the subtracting the GW signal aroundGW150914, as outlined in Sect. 6) is 192 out of 20,000, for a false alarm probability (FAP) of9.6× 10−3 or a significance of 2.34σ. Finally, we get a value of E, greater than that obtainedin LJ16 (viz. 0.84) for 22 out of 20,000 realizations, for a FAP of 1.1 × 10−3 correspondingto a significance of 3.06σ. This significance is about the same as found in LJ16.

8 Conclusions

We replicate the procedure in LJ16 [1], to see if we can independently corroborate their claimof a long duration low-amplitude signal at 3.2σ in the vicinity of GW150914 at the sametime lag (as GW150914). We implemented two different data conditioning procedures fordata within ± 2048 seconds of GW150914 (which lasted for about 0.2 seconds from 35 to 150Hz). The only difference with respect to the analysis in LJ16 is that we have used version2 of the calibrated strain data and applied notch filtering in the time domain, instead ofclipping in the frequency domain as in LJ16. Similar to LJ16, we calculated the Pearsoncross-correlation coefficient (C(t, τ, w)), and also its integral D(τ) for 0.1 and 0.2 secondwindows across the full ± 2048 seconds of data. LJ16 had found that D(τ) in this off-sourceregion is maximally correlated with CGW (τ, w) for the same time lag as GW150914, whereCGW (τ, w) is the Pearson cross-correlation coefficient for a time-window w around GW150914.They showed that this ancillary signal lasted between 1280 and 4050 seconds, where the zeropoint corresponds to 2048 seconds before GW150914. We roughly find the same trends in thebehaviour of CGW and D, using both the data conditioning procedures. Similar to LJ16, wefind a strong correlation in CGW and D at the same time lag as GW150914 (around 7.5 ms)in a 30-minute window after GW150914. We then reanalyzed the cross-correlation betweenCGW and D, after including the full data stream, but after removing the best-fit templatearound the GW signal. We find that the values of E for time lags close to 7.5 ms is about

– 13 –

the same as before. We also the statistical significance of obtaining a value greater than ourobserved cross-correlation to be about 2.5σ, which is roughly comparable to the significanceof 3.1σ found in LJ16.

As an extension of this method, we also evaluated the cross-correlation coefficient innon-overlapping 0.1/0.2 second windows in order to discern the existence of any other shortduration signal in the off-source region, for all physical time lags. We do not find any otherdata stretch, which shows a value of C in this region, which could be deemed statisticallysignificant.

We have made available our Python scripts containing all the codes to reproduce theresults at https://github.com/RahulMaroju/GW150914-analysis

Acknowledgments

This research has made use of data, software and/or web tools obtained from the GravitationalWave Open Science Center (https://www.gw-openscience.org), a service of LIGO Laboratory,the LIGO Scientific Collaboration and the Virgo Collaboration. LIGO is funded by the U.S.National Science Foundation. Virgo is funded by the French Centre National de RechercheScientifique (CNRS), the Italian Istituto Nazionale della Fisica Nucleare (INFN) and theDutch Nikhef, with contributions by Polish and Hungarian institutes. We thank Hao Liu forexplaining in detail all the technical details of LJ16. We are grateful to Soumya Mohanty forthe comments on the manuscript and to Malik Rakhmanov for helpful correspondence.

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